A unit used in electrical
engineering and acoustics to express the ratio between two values
with the same dimensions. The quantities compared may be two power
levels, two voltages, two sound pressure levels, and so on. Since the quantities in the ratio
always have the same dimensions, the dimensions cancel out; the decibel itself
is dimensionless. Some examples of other dimensionless units are the
radian and ppm.1 Symbol, dB, but see below.

A measurement in decibels can express an absolute magnitude, provided one side of the ratio
is a reference
level explicitly or implicitly specified. A large number of reference
levels, measuring several different properties, have been used. What level of
which property is often shown by adding a suffix to the dB symbol, for example,
“dBm”. Sometimes the
portion after “dB” is printed as a subscript, or follows as a
separate word, for example, “dB SPL”. In several cases the suffixes
have themselves become part of the names of units. Recording engineers, for
example, refer to “dee-bee-you”, the dBu.

The bel is named for Alexander Graham Bell (1847-1922).

The decibel is not an
SI unit, though the use of the decibel with
SI units is sanctioned by the CIPM.2 The
symbol for the decibel was originally “db”, but over time the influence of the
SI usage rules has been so strong that they are now applied to the decibel
symbol
history please: the first letter that represents a person's name in a symbol is capitalized, while the name of the unit is not. Compare watt, W.; pascal, Pa;
volt, V; hertz, Hz, etc. The lowercase “d” comes from the symbol for the metric
prefix “deci-”. Hence, dB.

The Bell System has adopted the name “decibel” for the “transmission unit,” based on a power ratio of 10.1. This is in accordance with the terminology for the decimal unit, the prefix “deci” being the usual one for indicating a one-tenth relation.3

The one-tenth in the definition of the decibel occurs in 10 to the
one-tenth power. That is not what deci- means in the metric system.

The decibel began as the transmission unit,
defined by researchers at AT&T to replace of the “mile
of standard cable.” a unit of power ratio used in telephone
engineering.1 One of the shortcomings of the mile of standard
cable was that it was frequency-dependent. The transmission unit was not, it was
purely a unit if power ratio.

The transmission unit was soon renamed the bel (for Bell)3, but the bel is
inconveniently large, and the decibel is also

Extending the decibel to voltage and current

power 10 log /p/p current and voltage as well (in other words, first
watts, later volts and amperes). In the context telephone system

standardized 600 impedances, and under those circumstances power is
proportional to the square root of the voltage or amperage. In logarithm, square
roots are , so became 2 times; 10 times log V/V or log .

Similarly for electric currents,

Later, as the
decibel spread beyond the confines of Bell Labs, the difference between 10 and 20
would become a source of confusion.

That the dBm is, in fact, a unit is demonstrated by the fact that the
calculation process can be run in reverse to get milliwatts (no question that that is a
unit!) from a measurement expressed in dBm. Notice that, without the m", that
would be impossible. 467 kilowatts and 1000 kilowatts

The Use grows

it was adopted as an international unit at the
First International Acoustical Conference (Paris, July 1937) for scales of energy and
pressure levels.2

Important documents which have been written and reviewed by men eminent in
their profession have contained statements which are demonstrable contradictions
of basic physical laws. Measurements of power magnitudes have been found to
yield results which have differed by several orders of magnitude from estimates
based on computation. These errors can be attributed directly to the practice of
expressing current ratios, or acoustic pressure ratios, in decibels when these
ratios are not the square roots of corresponding power ratios.

Horton (1954) page 551.

The writer, as chairman of the ASA C42 Subcommittee on
Definitions of
Communication Terms, has been bombarded with letters divided about equally
between pleas for extension of the db [sic] to new kinds of ratios and pleas
for strict limitation of the meaning.

E. I. Green.IRE Transactions,
April 1954, page 43.

The use of the term “decibel” in connection with a quantity other than
power is a violation of the original definition of the decibel. It has, however, become so general that it may have to be lived with, at least in the foreseeable
future.

Hartley 1955

A variety of other names have been proposed for the decibel, including
logit36,
decilit37,
decilog,
decomlog38 and
decilu. 39

The decibel was originally primarily used in Britain and the United
States; in continental Europe
the neper played the same role. In the early 21st
century, the CCU considered recommending adding the neper to the list of
SI units as a coherent unit of logarithmic decay, leaving the bel outside SI. To date nothing
has come of this effort.3

1. Rather than call these units dimensionless, some experts prefer to treat them as having the dimension 1.
Dimensionlessness is a very controversial subject among metrological
philosphers. Horton (1954), cited below, is a good example of willful
incomprehension of the subject.

37. V. V. L. Rao and S. Lakshminarayanan.
The Decilit: A New Name for the Logarithmic Unit of Relative Magnitudes.Journal of the Acoustical Society of America, vol. 27, issue 2,
page 376 (1955).
doi:10.1121/1.1907863

Power ratios for electric signals

In audio and broadcast engineering, for power of electric signals, the decibel is 10 times the common logarithm of the ratio of the
power of the signal being described to the power of the reference level. When
the meter reads "0 dB",
the signal being measured equals the reference level.

dBm

The reference level is 1 milliwatt across an impedance of 600 ohms. The “m” stands for
"milliwatt". The 600 ohms value came from standards in the telephone industry, the high-tech of the early 20th
century, in which maximizing power transfer by matching output and input
impedances was an important consideration. Note that a 0 dBm signal in a circuit
with an impedance of 600 ohms corresponds to 0.775 volt rms. A signal change
of −3 dBm is roughly a halving of the power.

dBm0

dBi

Used in engineering antennas. The "i" stands for "isotropic". imaginary
isotropic antenna, raditing euqally in all directiobs, withe the The
strenght of the radiation is measured in microwatts per square meter

dBd

Voltage ratios for electric signals

As tubes (valves) gave way to transistors, matching impedances became less important.
Audio engineers went from using decibels based on power to those based on voltage. For
voltages, the decibel is 20 times the common logarithm of the ratio of voltage
being measured to the reference voltage.

The reference level is 1 volt rms across any impedance. To convert dBV to
dBu, add 2.2 dB. Consumer audio gear is designed for an normal input
level of −10 dBV, which corresponds to 0.316 volt rms. This voltage
level arose because it was the optimal maximum level for a signal fed directly
to an electron tube (valve to Brits), which was a practice in consumer
equipment.

dBv

The reference level is 0.775 volt rms across any impedance. The 0.775 volt
value comes from the definition of dBm, since it is the voltage when a 0 dBm
sine wave is fed into 600 ohms. This symbol was too easily confused with dBV, and so
was renamed dBu.

Some writers do not observe the distinction between the upper
and lower case V and treat both dBV and dBv as referenced to 1 volt rms.

The reference level is 0.775 volt rms across any impedance.
See dBm above for the origin of the value. The “u”
stands for unterminated. Professional audio equipment is designed for
a normal input level (“line level”) of +4 dBu, which corresponds
to 1.23 volts rms. A signal change of −6 dBu is about a halving of the
voltage.

“FS” stands for “full scale.” A unit used in monitoring signal levels in
digital signal processing, such as digital
audio. To record audio (or any analog signal) digitally, the signal level is
measured at equal, small intervals and the value recorded as a number. For
audio this requires recording as many as 192,000 numbers each second, so it is
necessary to choose a way of representing numbers that a computer can process
very quickly and efficiently. All such systems for representing numbers have a
biggest number that can be represented (and also a smallest negative number,
what follows applies to negative numbers as well). This is the full scale point.
If the level of the analog signal is greater than the level assigned to the
biggest possible number, there is no way of recording its actual value. Every
level greater than the one assigned to the largest possible number is usually
simply recorded as the largest possible number. The signal is "clipped." The
dBFS scale provides a way of indicating how close one is coming to this
undesirable situation.

In such a system, the maximum
level before clipping of a sine wave is -3 dBFS.

Further, AES Information Document for Digital audio engineering – Personal
computer audio quality measurements, AES-6id-2006 defines Decibels, Fullscale
(dB FS): “Digital signal rms amplitude expressed as a level in decibels
relative to full-scale amplitude (20 times the common logarithm of the amplitude
over the full-scale amplitude [defined as the ‘rms amplitude of a 997 Hz sine
wave in the digital domain whose positive peak value reaches the positive
digital full scale, leaving the negative maximum code unused.’]). Note that dB
FS expresses a signal level of a digital signal and should not be used to
express the signal level of an analog signal.”

Reflected radar signal level

dBZ

In meteorology, a measure of the strength of a radar signal reflected off a
distant object, such as clouds and falling rain or snow, compared to the
strength of the emitted signal. The reference level is 1
millimeter6 / meter3, which equals 1 cubic micrometer. See
VIP levels.